Operation on 2 different complex numbers

Addition	${\displaystyle i+i=2i}$
Subtraction	${\displaystyle i-i=0}$
Multiplication	${\displaystyle i\times i={\sqrt {-1}}{\sqrt {-1}}=1}$
Division	${\displaystyle {\frac {i}{i}}=1}$

Operation on complex numbers qnd its conjugate

Addition	${\displaystyle i+(-i)=0}$
Subtraction	${\displaystyle i-(-i)=2}$
Multiplication	${\displaystyle i\times (-i)=-1}$
Division	${\displaystyle {\frac {i}{(-i)}}=-1}$

Power of imaginary numbers

${\displaystyle i={\sqrt {-1}}}$

${\displaystyle i^{2}={\sqrt {-1}}{\sqrt {-1}}=1}$

${\displaystyle i^{3}={\sqrt {-1}}{\sqrt {-1}}{\sqrt {-1}}=-1{\sqrt {-1}}=-i}$

${\displaystyle i^{4}={\sqrt {-1}}{\sqrt {-1}}{\sqrt {-1}}{\sqrt {-1}}=1}$

Hence,

${\displaystyle i^{n}=\pm 1}$

${\displaystyle i^{n}=1}$ . Even power

${\displaystyle i^{n}=\pm i}$ . Odd power